Stationarity, soft ergodicity, and entropy in relativistic systems

Recent molecular dynamics simulations show that a dilute relativistic gas equilibrates to a Juettner velocity distribution if ensemble velocities are measured simultaneously in the observer frame. The analysis of relativistic Brownian motion processes, on the other hand, implies that stationary one-particle distributions can differ depending on the underlying time-parameterizations. Using molecular dynamics simulations, we demonstrate how this relativistic phenomenon can be understood within a deterministic model system. We show that, depending on the time-parameterization, one can distinguish different types of soft ergodicity on the level of the one-particle distributions. Our analysis further reveals a close connection between time parameters and entropy in special relativity. A combination of different time-parameterizations can potentially be useful in simulations that combine molecular dynamics algorithms with randomized particle creation, annihilation, or decay processes.Comment: 4 page

Nonlocal observables and lightcone-averaging in relativistic thermodynamics

The unification of relativity and thermodynamics has been a subject of considerable debate over the last 100 years. The reasons for this are twofold: (i) Thermodynamic variables are nonlocal quantities and, thus, single out a preferred class of hyperplanes in spacetime. (ii) There exist different, seemingly equally plausible ways of defining heat and work in relativistic systems. These ambiguities led, for example, to various proposals for the Lorentz transformation law of temperature. Traditional 'isochronous' formulations of relativistic thermodynamics are neither theoretically satisfactory nor experimentally feasible. Here, we demonstrate how these deficiencies can be resolved by defining thermodynamic quantities with respect to the backward-lightcone of an observation event. This approach yields novel, testable predictions and allows for a straightforward-extension of thermodynamics to General Relativity. Our theoretical considerations are illustrated through three-dimensional relativistic many-body simulations.Comment: typos in Eqs. (12) and (14) corrected, minor additions in the tex

The crosstalk between FGF21 and GH leads to weakened GH receptor signaling and IGF1 expression and is associated with growth failure in very preterm infants.

BACKGROUND: Fibroblast growth factor 21 (FGF21) is an essential metabolic regulator that adapts to changes in nutritional status. Severe childhood undernutrition induces elevated FGF21 levels, contributing to growth hormone (GH) resistance and subsequent linear growth attenuation potentially through a direct action on chondrocytes. METHODS: In this study, we assessed expression of the components of both GH and FGF21 pathways in rare and unique human growth plates obtained from children. Moreover, we investigated the mechanistic interplay of FGF21 on GH receptor (GHR) signaling in a heterologous system. RESULTS: Chronic FGF21 exposure increased GH-induced GHR turnover and SOCS2 expression, leading to the inhibition of STAT5 phosphorylation and IGF-1 expression. The clinical significance of FGF21 signaling through GH receptors was tested in nutritionally driven growth failure seen in very preterm (VPT) infants right after birth. VPT infants display an immediate linear growth failure after birth followed by growth catch-up. Consistent with the in vitro model data, we show that circulating FGF21 levels were elevated during deflection in linear growth compared to catch-up growth and were inversely correlated with the length velocity and circulating IGF1 levels. CONCLUSIONS: This study further supports a central role of FGF21 in GH resistance and linear growth failure and suggests a direct action on the growth plate

Relativistic diffusion processes and random walk models

The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As well-known, the Gaussian transition probability density function (PDF) of this process is in conflict with special relativity, as it permits particles to propagate faster than the speed of light. A frequently considered alternative is provided by the telegraph equation, whose solutions avoid superluminal propagation speeds but suffer from singular (non-continuous) diffusion fronts on the light cone, which are unlikely to exist for massive particles. It is therefore advisable to explore other alternatives as well. In this paper, a generalized Wiener process is proposed that is continuous, avoids superluminal propagation, and reduces to the standard Wiener process in the non-relativistic limit. The corresponding relativistic diffusion propagator is obtained directly from the nonrelativistic Wiener propagator, by rewriting the latter in terms of an integral over actions. The resulting relativistic process is non-Markovian, in accordance with the known fact that nontrivial continuous, relativistic Markov processes in position space cannot exist. Hence, the proposed process defines a consistent relativistic diffusion model for massive particles and provides a viable alternative to the solutions of the telegraph equation.Comment: v3: final, shortened version to appear in Phys. Rev.

Dynamics, scaling behavior, and control of nuclear wrinkling

The cell nucleus is enveloped by a complex membrane, whose wrinkling has been implicated in disease and cellular aging. The biophysical dynamics and spectral evolution of nuclear wrinkling during multicellular development remain poorly understood due to a lack of direct quantitative measurements. Here, we combine live-imaging experiments, theory, and simulations to characterize the onset and dynamics of nuclear wrinkling during egg development in the fruit fly, Drosophila melanogaster, when nurse cell nuclei increase in size and display stereotypical wrinkling behavior. A spectral analysis of three-dimensional high-resolution data from several hundred nuclei reveals a robust asymptotic power-law scaling of angular fluctuations consistent with renormalization and scaling predictions from a nonlinear elastic shell model. We further demonstrate that nuclear wrinkling can be reversed through osmotic shock and suppressed by microtubule disruption, providing tunable physical and biological control parameters for probing mechanical properties of the nuclear envelope. Our findings advance the biophysical understanding of nuclear membrane fluctuations during early multicellular development.Comment: Main text: 10 pages, 3 figures. SI: 19 pages, 10 figures, 1 tabl

Relativistic diffusion of elementary particles with spin

We obtain a generalization of the relativistic diffusion of Schay and Dudley for particles with spin. The diffusion equation is a classical version of an equation for the Wigner function of an elementary particle. The elementary particle is described by a unitary irreducible representation of the Poincare group realized in the Hilbert space of wave functions in the momentum space. The arbitrariness of the Wigner rotation appears as a gauge freedom of the diffusion equation. The spin is described as a connection of a fiber bundle over the momentum hyperbolic space (the mass-shell). Motion in an electromagnetic field, transport equations and equilibrium states are discussed.Comment: 21 pages,minor changes,the version published in Journ.Phys.

Deformed Algebras from Inverse Schwinger Method

We consider a problem which may be viewed as an inverse one to the Schwinger realization of Lie algebra, and suggest a procedure of deforming the so-obtained algebra. We illustrate the method through a few simple examples extending Schwinger's $su(1,1)$ construction. As results, various q-deformed algebras are (re-)produced as well as their undeformed counterparts. Some extensions of the method are pointed out briefly.Comment: 14 pages, Jeonju University Report, Late

The Effects of Earthquakes and Fluids on the Metamorphism of the Lower Continental Crust

Rock rheology and density have first‐order effects on the lithosphere's response to plate tectonic forces at plate boundaries. Changes in these rock properties are controlled by metamorphic transformation processes that are critically dependent on the presence of fluids. At the onset of a continental collision, the lower crust is in most cases dry and strong. However, if exposed to internally produced or externally supplied fluids, the thickened crust will react and be converted into a mechanically weaker lithology by fluid‐driven metamorphic reactions. Fluid introduction is often associated with deep crustal earthquakes. Microstructural evidence, suggest that in strong highly stressed rocks, seismic slip may be initiated by brittle deformation and that wall‐rock damage caused by dynamic ruptures plays a very important role in allowing fluids to enter into contact with dry and highly reactive lower crustal rocks. The resulting metamorphism produces weaker rocks which subsequently deform by viscous creep. Volumes of weak rocks contained in a highly stressed environment of strong rocks may experience significant excursions toward higher pressure without any associated burial. Slow and highly localized creep processes in a velocity strengthening regime may produce mylonitic shear zones along faults initially characterized by earthquake‐generated frictional melting and wall rock damage. However, stress pulses from earthquakes in the shallower brittle regime may kick start new episodes of seismic slip at velocity weakening conditions. These processes indicate that the evolution of the lower crust during continental collisions is controlled by the transient interplay between brittle deformation, fluid‐rock interactions, and creep flow

Notulae to the Italian native vascular flora: 2

In this contribution new data concerning the Italian distribution of native vascular flora are presented. It includes new records, exclusions, and confirmations to the Italian administrative regions for taxa in the genera Arctostaphylos, Artemisia, Buglossoides, Convolvulus, Crocus, Damasonium, Epipogium, Ficaria, Filago, Genista, Heptaptera, Heracleum, Heteropogon, Hieracium, Myosotis, Ononis, Papaver, Pilosella, Polygonum, Pulmonaria, Scorzonera, Silene, Trifolium, Vicia and Viola

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte